I think we can predict what will happen based on what happened to Usenet.
No single authority "censored" usenet articles. People posted what they wanted. It ended up as an ocean of spam, abuse and off-topic articles.
That's what the Texas law will entail. I think Abbott and Paxton didn't understand the consequences, or are gambling on a situation like what happened to radio, TV and newspapers in the 1990s after the "Fairness Doctrine" went away. Abbott and Paxton may hope that an informal cartel of conservative owners will let conservative/Republic viewpoints run wild, while behind the scenes or under the table manipulation suppresses liberal/other viewpoints, just like what happened to broadcast TV, radio and newspapers.